面对Hartree-Fock对称性困境的量子Monte Carlo：氢环的情况
Quantum Monte Carlo facing the Hartree-Fock symmetry dilemma: The case of hydrogen rings
摘要：
当在量子蒙特卡罗计算中使用Hartree-Fock（HF）试探波函数时，在HF不稳定性的情况下，在较高HF能量的自适应解和较低HF能量的自适应破缺解之间进行选择时，人们面临HF对称性困境。在这项工作中，我们已经研究了HF对称性的困境，目前单重态不稳定性的氢环足够大的环。我们已经发现，在变分蒙特卡罗和固定节点扩散蒙特卡罗中，自适应HF波函数给出了较低的能量。这表明，自适应波函数比破缺波函数具有更精确的节点，空间对称性是选择好的试波函数的重要标准。
英文摘要：
When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetry-adapted solution of higher HF energy and symmetry-broken solutions of lower HF energies. In this work, we have examined the HF symmetry dilemma in hydrogen rings which present singlet instabilities for sufficiently large rings. We have found that the symmetry-adapted HF wave function gives a lower energy both in variational Monte Carlo and in fixed-node diffusion Monte Carlo. This indicates that the symmetry-adapted wave function has more accurate nodes than the symmetry-broken wave functions, and thus suggests that spatial symmetry is an important criterion for selecting good trial wave functions.
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